Geometry Problem 1131: Triangle Area, Two Cevians, Equal Product of Areas. Level: High School, SAT Prep, Honors Geometry, College, Math Education

In a triangle ABC of area S, cevians AD and CE meet at F (figure below). If S₁, S₂, and S₃ are the areas of triangles BDE, DEF, and AFC, respectively, prove that: S.S₂ = S₁.S₃.